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Acta Biotheoretica

, Volume 48, Issue 1, pp 47–63 | Cite as

Pattern Formation in a Nonlinear Membrane Model for Epithelial Morphogenesis

  • Larry A. Taber
Article

Abstract

A theoretical model is presented for pattern formation in an epithelium. The epithelial model consists of a thin, incompressible, viscoelastic membrane on an elastic foundation (substrate), with the component cells assumed to have active contractile properties similar to those of smooth muscle. The analysis includes the effects of large strains and material nonlinearity, and the governing equations were solved using finite differences. Deformation patterns form when the cells activate while lying on the descending limb of their total (active + passive) stress-stretch curve. Various one-dimensional and two-dimensional simulations illustrate the effects of spatial and temporal variations in passive stiffness, as well as the effects of foundation stiffness and stretch activation. The model can be used to examine the mechanical aspects of pattern formation in morphogenetic processes such as angiogenesis and myocardial trabeculation.

Keywords

Pattern Formation Elastic Foundation Active Contractile Material Nonlinearity Deformation Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Larry A. Taber
    • 1
  1. 1.Department of Biomedical EngineeringWashington UniversitySt. LouisUSA. Tel

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